Enhancing Text Analysis via Dimensionality Reduction
David G. Underhill and Luke K. McDowell
Dept. Computer Science, U.S. Naval Academy
572M Holloway Rd, Annapolis, MD 21402
(410) 293-6800
david.g.underhill@gmail.com,lmcdowel@usna.edu
Abstract
Many applications require analyzing vast amounts of
textual data, but the size and inherent noise of such data
can make processing very challenging. One approach to
these issues is to mathematically reduce the data so as
to represent each document using only a few dimensions.
Techniques for performing such “dimensionality reduction”
(DR) have been well-studied for geometric and numerical
data, but more rarely applied to text. In this paper, we examine the impact of five DR techniques on the accuracy of
two supervised classifiers on three textual sources. This task
mirrors important real world problems, such as classifying
web pages or scientific articles. In addition, the accuracy
serves as a proxy measure for how well each DR technique
preserves the inter-document relationships while vastly reducing the size of the data, facilitating more sophisticated
analysis. We show that, for a fixed number of dimensions,
DR can be very successful at improving accuracy compared
to using the original words as features. Surprisingly, we
also find that one of the simplest DR techniques, MDS, is
among the most effective. This suggests that textual data
may often lie upon a linear manifold where the more complex non-linear DR techniques do not have an advantage.
1
Introduction
Individuals, companies, and governments are surrounded by millions of web pages, communications, and
other documents that are potentially relevant, yet in danger
of being overlooked amongst all the other data. Analyzing such data is complicated by its representation as natural
language text, rather than as a structured database record
or a numerical measurement. While such documents can be
analyzed with sophisticated natural language processing applications, the challenges of fully understanding text and the
daunting amount of data often make statistical text mining
techniques more attractive. Such techniques typically en-
David J. Marchette and Jeffrey L. Solka
Code Q20, NSWCDD
Dahlgren, VA 22448
(540) 653-1910
{david.marchette,jeffrey.solka}@navy.mil
code the content of a document as a vector with thousands
of dimensions, one for each useful word in the corpus.
One possible approach to simplifying the analysis of
such high dimensional data is to apply some form of “dimensionality reduction” (DR). Techniques for DR all seek
to take input points and represent them in a much smaller
number of dimensions, while retaining important characteristics of the original data. These techniques have been
primarily applied to numerical data, particularly data representing geometric shapes. With a few exceptions (see Section 5), they have not been as well studied for textual data.
This paper analyzes how traditional and more recent
DR techniques might be profitably applied to textual data.
In particular, we evaluate five such techniques: Principal
Components Analysis (PCA) [8], Multi-dimensional Scaling (MDS) [11], Isomap [5], Locally Linear Embedding
(LLE) [15], and Lafon’s Diffusion Maps (LDM) [4]. To
measure their effectiveness with text, we perform document
classification using both linear and k-nearest-neighbor classifiers. Document classification is a fundamental and useful
text analysis task (e.g., for categorizing newly discovered
web pages based on previously labeled pages). In addition,
our document classification results indicate how well each
DR technique has preserved the interesting inter-document
relationships. Thus, these results help to predict which DR
techniques might be best suited for pre-processing before
performing more complex analysis tasks such as Literaturebased discovery [14, 17] or sentiment analysis [13].
Our contributions are as follows. First, we demonstrate
that, for a fixed number of dimensions, applying DR before
classification can significantly improve accuracy. This enables classifiers to be more efficient and reduces the impact
of noisy dimensions on the results. Second, we show the
surprising result that some of the simplest techniques perform best. In particular, we find that MDS and the closely
related Isomap have the most reliable performance, almost
always yielding the best performance compared to other
DR techniques. In addition, both MDS and Isomap are
frequently able to match or approach the performance of
a naive data representation that uses thousands of dimensions when they use only 10-20 such dimensions. Finally,
using specially modified versions of one of our data sets,
we demonstrate that the advantages of MDS and Isomap
are even more pronounced when classification is more difficult. Overall, our results show that simple techniques can be
highly effective at reducing textual data while maintaining
its most interesting properties.
The following section explains the DR techniques that
we evaluate. Section 3 outlines our experimental method
and Section 4 presents our results. Section 5 compares these
findings with related work, and Section 6 concludes.
2
Table 1. Data Sets
Name
Science News
Science & Tech.
Google News
1. Principal Components Analysis (Linear) - PCA is a
correlation-based technique that chooses a set of representative dimensions called the principal components
based on the degree of variation that they capture from
the original data [8]. In particular, PCA computes the
output points by performing a singular value decomposition (SVD) on the document covariance matrix and
then multiplies the resulting eigenvectors with their
corresponding eigenvalues.
2. Metric Multidimensional Scaling (Linear) - MDS
focuses on preserving distances between pairs of
points [20]. The input is a matrix containing pairwise
distances between the original points. MDS performs
an eigenvalue decomposition on this matrix in a way
that embeds the points in a smaller space while maintaining the relative pairwise relationships [11].
3. Isomap (Non-Linear) - Like MDS, Isomap seeks
to preserve the pairwise distances between input
points [1]. Its matrix, however, is based on the
geodesic distance, which is computed by connecting
# Docs
1047
658
3028
Avg. Doc. Size
8000 chars
2500 chars
4000 chars
points in a computed nearest-neighbors graph. This
process can more accurately represent some local patterns [5]. The final result is produced by running MDS
on the modified distance matrix.
4. Lafon’s Diffusion Maps (Non-Linear) - LDM performs non-linear transformations on an initial interpoint distance matrix in a way that helps accentuate local relationships [4]. In particular, LDM tries to more
strongly connect those points that are connected by
multiple paths in a nearest-neighbors graph. As with
PCA, the final step is a singular value decomposition.
Background
Dimensionality reduction can take many different forms.
In feature selection, DR consists simply of eliminating less
significant features from the data set, e.g., by information
gain [21]. We focus instead on DR for feature extraction,
where new features are created based on some (possibly
complex) transformation of the input features. DR methods
can also be divided into supervised and unsupervised techniques, where the supervised techniques are informed by labels associated with the input instances (or documents). Because we wish to facilitate text mining applications where
such labels are often not known (e.g., with the aforementioned sentiment analysis), we focus on unsupervised DR
techniques. Finally, a DR technique is linear if a linear
transformation converts an input data point to the reduced
feature space; otherwise, the technique is non-linear.
We consider the following unsupervised DR techniques:
Categories
8
7
5
5. Locally Linear Embedding (Non-Linear) - LLE
uses geometric intuition and an assumption that
high-dimensional data actually resides on some
low-dimensional manifold within the large input
space [15]. A reduced embedding is found by translating, rotating, and scaling the existing data based on
weights that maintain geometric properties present in
a graph of nearest neighbors. The transformed data is
then reduced via an eigenvalue decomposition.
3
Methodology
In our experiments, we begin with a collection of documents, encode the documents into a term-document matrix,
then perform dimensionality reduction on this large matrix.
Using the reduced matrix, we then classify each document
into one of several known categories. Finally, we evaluate
the results. Below we elaborate on each of these steps.
3.1 Data Sets
Table 1 shows the three datasets that we used for our
experiments. The Science News [16] and Google News
(drawn from articles on news.google.com) corpuses each
contain over 1,000 articles distributed among a number of
well-defined categories. S&T [16] is much more difficult
to classify because there is much less information per article - some articles only contain 2-3 sentences. Furthermore,
S&T has the smallest ratio of articles to categories.
3.2 Document Encoding
To facilitate further processing, our documents must first
be encoded. Typically for text mining, a corpus is encoded
similar trends; we report results for one setting that
worked well for all DR techniques (k = 9).
as a matrix where each document is described by a row
in a matrix. There are a number of possible matrices and
ways to compute them, but based on previous work [12, 16]
we adopt the following straight-forward scheme. In this
method, each column is a feature that corresponds to a single word found in the corpus. Cell (i, j) is then the TFIDF [3] score for word j in document i, defined as:
t/T
Ti,j =
lg(D/d)
2. Linear Classifier: Our second classifier assumes that
each feature is normally distributed, and makes a classification decision based on a linear combination of the
features. In particular, the likelihood of document i being in category k is computed as:
f (xi , ĉk ) =
where t is the number of times word j appears in document
i, T is the total number of words in document i, d is the
total number of documents that contain word j, and D is
is the total number of documents in the corpus. The resulting matrix is known as a (weighted) Term-Document Matrix
(TDM). In our implementation, before computing the TDM
we perform word stemming and also discard any word that
does not occur at least three times in the corpus.
3.3
3.4
Classifiers
We evaluated with three commonly-used classifiers:
1. k-Nearest Neighbor Classifier (kNN): kNN assigns
a category to a document based on the class(es) of the
k closest instances (nearest neighbors) in the training
data as defined by a similarity function. Our implementation computed similarity using cosine distance
and picked the most likely category using similarityweighted voting among the closest neighbors. Experimentally, we found that different values of k produced
(2π)
1
· |Σ|
1
2
·e− 2 (xi −µk )×Σ
−1
×(xi −µk )T
where N is the number of features, xi is the row vector representing the document being classified, µk is
the vector of feature means for category k from the
training set, and Σ is the inter-feature covariance matrix. For the linear classifier, the same Σ is used for
every category, which results in two categories being
separated by a hyperplane in the feature space.
3. Quadratic Classifier: The quadratic classifier is like
the linear classifier, but uses category-specific covariance matrixes. Consequently, two categories are separated by more complex non-linear functions in the feature space. We found similar trends as with the linear
classifier and omit details for lack of space.
Dimensionality Reduction
The encoded TDM has 600-3000 rows (one for each document) and 5000-11000 columns (one for each stemmed
word in the corpus). We next use dimensionality reduction
to significantly reduce this number of columns (or features).
In our experiments, we use the five DR techniques described in Section 2. We implemented each technique in
Java, then validated each against existing Matlab or R code
that we obtained from others. Isomap and LLE require a
choice of how many closest neighbors to consider when
constructing the nearest neighbor graph; experimentally we
found that using 10 neighbors yielded good results.
Each technique outputs the most significant dimensions
first, enabling us to examine the impact of only using the
first M dimensions for classification. In addition, we also
compared against two variants that performed no DR. First,
None-rand randomly selects and uses M features from the
unmodified TDM matrix. Second, None-sort also uses M
unmodified features, but selects the N features with the
highest average TF-IDF score (the more significant words).
These two variants highlight the potential classification performance easily obtainable without performing any DR.
1
N
2
We measure classification accuracy, which is the percentage
of documents that were assigned to the correct category. All
experiments used a leave-one-out procedure for testing.
4
Experimental Results
Table 2 shows the classification accuracy achieved (as a
percentage) after encoding a corpus, performing DR, and
then applying the kNN classifier (Table 3 gives results for
“Linear”). Each row gives the results for one DR technique,
or when using None-sort or None-rand (see Section 3.3).
Within a corpus, the column labeled “All” shows the results obtained when the classifier is provided with all available features for each document. For None-sort or Nonerand, this is every (stemmed) word (5000-11000 depending
on the corpus). For the DR techniques, “All” corresponds
to using every dimension considered significant enough to
be produced by the DR algorithm; this varies from 700 to
3300 dimensions depending on the technique and corpus.
In addition, since each DR technique outputs the final dimensions sorted by their perceived significance, we also
present results where the classifier uses only the first 5, 10,
20, 50, 100, or 500 dimensions. For instance, reducing Science News with PCA, then classifying using kNN with only
the best 20 dimensions yields an accuracy of 81%. Results
within 2% of the best for each column are shown in bold.
Before presenting our primary results, we first explain
a few trends. First, performance generally increases as
Num. dims.
PCA
MDS
Isomap
LLE
LDM
None-sort
None-rand
Num. dims.
PCA
MDS
Isomap
LLE
LDM
None-sort
None-rand
5
77
72
70
65
65
34
13
5
77
63
66
49
59
29
08
10
81
78
76
70
74
41
14
Table 2. Results with the kNN classifier
Science News
Science & Technology
20 50 100 500 All
5 10 20 50 100 500 All
81 80 76 47 39
33 45 48 52 48 29 11
78 78 77 78 78
56 59 60 61 59 64 64
76 76 77 73 73
57 59 61 60 61 58 58
75 75 74 28 17
26 26 25 24 24 23 22
76 75 75 17 19
23 26 24 28 34 13 06
54 66 67 75 78
27 34 41 47 53 59 61
17 22 36 43 78
12 14 15 24 26 39 61
5
24
82
83
78
22
30
18
10
25
86
86
80
23
35
19
Google News
20 50 100 500
26 29 32 34
88 89 89 88
86 87 87 85
83 83 84 82
26 57 60 55
50 68 73 83
23 27 38 57
All
21
88
84
72
51
89
89
10
82
74
71
60
71
39
19
Table 3. Results with the Linear classifier
Science News
Science & Technology
20 50 100 500 All
5 10 20 50 100 500 All
84 87 93 99 99
31 37 45 58 65 95 95
77 84 87 98 99
50 58 64 72 79 99 99
77 81 83 99 99
51 57 60 67 76 95 95
70 76 81 96 99
17 18 31 36 41 89 89
76 82 86 98 99
22 21 25 34 53 90 90
48 51 69 98 17
23 30 43 54 68 99 07
16 34 43 91 17
09 12 15 34 43 72 07
5
20
78
78
54
25
38
28
10
22
79
80
58
26
46
25
Google News
20 50 100 500
23 31 34 38
82 85 89 95
80 82 85 93
64 70 75 87
27 47 53 62
54 68 76 91
27 39 47 72
All
61
99
98
97
77
39
39
the number of dimensions increases. When the number
of dimensions is very large (500 or “All”), however, performance may decrease, particularly with kNN. We note
that kNN performance in this region would likely improve
with a weighted similarity function, though the general
trends among DR techniques would be the same. Linear
is less susceptible to this problem, because it naturally detects when a particular feature is not helpful in discriminating among the classes. Thus, even when using all dimensions output by a particular DR technique (at most about
1000), performance is maintained or improved. However,
even Linear can get overwhelmed by many noisy dimensions [18], as occurs with None-sort and None-rand, where
“All” corresponds to 5000-11000 dimensions.
Result 1. Compared to other DR techniques, MDS and
Isomap yield the most consistent and reliable classification
performance. On S&T and Google News, MDS and Isomap
dominate. For instance, with 100 dimensions MDS and
Isomap improve on other DR techniques by between 1137% for kNN and 11-38% for Linear. For these data sets,
MDS is always within 2% of the best results, and Isomap
almost always does just as well.
Science News is somewhat of an exception. For this corpus PCA yielded the best performance, for both kNN and
Linear, especially when the number of dimensions is small.
For instance, with just 5 dimensions, PCA achieves 77% accuracy with Linear, while the next best is 66% with Isomap.
However, MDS and Isomap improve more rapidly as the
number of dimensions increases. Hence by 50 dimensions
MDS is within 3% of PCA, and Isomap is not far behind.
Furthermore, with kNN, MDS and Isomap do not exhibit
large drops in performance when using “All” dimensions,
unlike PCA, LLE, and LDM. In general, performance with
kNN on DR-processed data starts to drop after 100 dimensions, because the newer (less significant) dimensions have
more noise. Since our classifier uses an unweighted similarity function, these dimensions have as much impact as
the first dimensions, and the noise causes accuracy to decrease. The MDS algorithm, however, naturally recognizes
when there is little benefit to be added from additional dimensions, and as a result they take on very small values that
have little impact on the similarity calculations. Isomap utilizes MDS as part of its processing and thus inherits this
benefit. The net effect is that MDS and Isomap are very
reliable performers across the whole range of reduced dimensions.
In contrast, PCA and LDM, the two SVD-based techniques, both perform very poorly on S&T and Google News
when the number of dimensions is small. These techniques
appear to be more sensitive to the smaller amounts of data
per instance in these data sets (see Table 1). Despite this
common property, the two data sets yield significantly different performance. On Google News, peak performance
for both kNN and Linear reaches over 80% with just 10
dimensions. This can be attributed to the data set having
just five well-separated categories evenly split among over
3,000 articles. Science and Technology, on the other hand,
has seven categories and is unevenly distributed over just
658 articles. As a result, S&T needs 500 dimensions to get
over 80% accuracy with Linear and peaks at 64% for kNN.
Result 2. Compared to not performing DR, applying DR
before classification can greatly improve the accuracy obtainable with a given number of dimensions. Using MDS
or Isomap almost always improved accuracy compared to
None-sort or None-rand with the same number of dimensions. For instance, with Linear on Science News with
100 dimensions, using the raw words (None-rand) yielded
an accuracy of just 43%. Choosing 100 good words with
None-sort improved accuracy, but only to 69%. MDS or
Isomap, however, reached 83-87%. For PCA, LLE, and
LDM, this improvement held true for Science News, but
usually not for the more challenging S&T or Google News.
Result 3. The best DR techniques can enable very strong
accuracy using a small number of dimensions. With kNN,
MDS with just 10-20 dimensions achieves nearly the same
accuracy obtained by any DR or no-DR variant with any
number of dimensions. For instance, MDS with 20 dimensions on Google News has an accuracy of 88%, compared to
the best found with kNN of 89%. Isomap behaves similarly.
Linear requires many more dimensions (500 or more)
to reach its peak performance, though that level is always
higher than with kNN. However, MDS and Isomap can still
achieve very solid performance with fewer dimensions. For
instance, with 100 dimensions MDS reaches 87% for Science News, 79% for S&T, and 89% for Google News.
Result 4. MDS and Isomap’s advantages may be even more
pronounced on more difficult data sets. To further investigate the situations where MDS and Isomap perform best
with regards to classification, we created three variants of
the Science News data set. SN2 is a subset of Science
News that contains only Medicine and Astronomy articles two well-separated categories. SN4-Sep contains four fairly
well separated categories: Astronomy, Medicine, Earth Sciences, and Life Sciences. Finally, SN4-OL contains four
categories with collectively more topic overlap: Medicine,
Life Sciences, Behavior, and Anthropology.
In general, we found consistent results as before. Table 4 summarizes the results obtained when using 50 dimensions. SN2 is a much easier task, and almost every
technique gets near perfect accuracy. SN4-Sep is somewhat
harder, but still yields better results than with the original
Science News, and every DR technique yields an accuracy
above 80%. With the more difficult SN4-OL, however, PCA
drops from 86-89% to just 31-43%. LDM suffers similar
losses. MDS and Isomap, however, decline by only 1-4%.
So while every DR technique did well on the easier
SN2 and SN4-Sep corpuses, only MDS and Isomap maintained accuracy over 80% on SN4-OL (though LLE was
close). Thus, when combined with our results from S&T
and Google News, we observe that MDS and Isomap perform at or near the best observed levels, but particularly
dominate when the the analysis is complicated by shorter
documents or less well-separated categories.
Table 4. Sci. News Variations (# dims. = 50)
Corpus
PCA
MDS
Isomap
LLE
LDM
None-sort
None-rand
5
kNN
SN2 SN4-Sep SN4-OL
98
99
99
99
98
99
85
86
85
82
84
82
81
68
43
81
83
78
44
69
44
Linear
SN2 SN4-Sep SN4-OL
99
99
99
99
99
98
83
89
89
88
87
89
87
74
31
89
86
84
50
76
54
Related Work and Discussion
As previously discussed, DR has frequently been applied
to data sources such as images [1, 5, 15] and biological
data [7]. However, the uses of DR for text, particularly
the sorts of unsupervised DR methods that we explore in
this paper, have not been nearly as extensive. For instance,
van der Maaten et al. [19] present a thorough analysis of
classification performance using twelve DR techniques on
seven data sets, but only one data set is textual. In addition,
they do not examine the impact of different numbers of dimensions for the text corpus, do not consider perturbing the
corpus, and do not evaluate MDS. Nonetheless, it is useful
to make some limited comparisons between our results. We
both find that more complex techniques such as LLE and
LDM do not usually improve over simpler techniques like
PCA. However, PCA performs very well for their data sets,
particularly on the one text corpus (where it is the best unsupervised technique). Our results suggest that PCA may
indeed perform very well on some textual data (e.g., Science News), but poorly on more challenging data sets such
as S&T.
Kim et al. [10] describe alternative DR techniques that
can reduce the number of features needed to perform text
classification. These techniques, however, require that the
words in the data set already be clustered together into logical groups. Karypis and Han [9] explored how to expand
concept indexing, an alternative DR technique, to exploit
known classes of documents. For this one supervised technique, they demonstrate a small improvement in classification accuracy when using the reduced feature space. Bingham and Mannila [2] compare a PCA-like DR technique
against a computationally efficient approach based on random projection, and find that the simpler approach is able
to achieve comparable performance. However, for text they
evaluate only one DR technique, use only one corpus, and
evaluate distortion error rather than classification accuracy.
In contrast to the above work, we evaluate classification
accuracy using five DR techniques on three distinct corpuses. In addition, we do not require that any class labels or
word cluster information be provided to the DR algorithms.
6
Conclusions
This paper has examined how pre-processing with dimensionality reduction could improve text analysis, using
classification accuracy to measure performance. Of the five
DR techniques that we considered, all were able to achieve
substantial improvements compared to not performing DR,
under some conditions. However, MDS and the closely
related Isomap proved to be the best overall performers.
These two techniques consistently out-performed the noDR variants that we considered, and were able to achieve
strong accuracy using just a small number of dimensions.
MDS’s ability to out-perform more recent and more
complex techniques such as LDM was surprising. This
suggests that, at least for the corpuses we considered, this
textual data lies on a linear manifold for which the more
complex non-linear techniques do not hold an advantage.
In addition, we found that LDM, as well as older techniques such as PCA and LLE, had particular trouble with
corpuses where the documents were smaller or belonged
to less well separated categories. Both MDS and Isomap,
however, maintained good performance under these situations. Future work should verify these findings with additional data sets and other classifiers. Additionally, it would
be worthwhile to more precisely characterize the corpuses
for which MDS and Isomap hold an advantage.
The ability to reduce input documents while preserving significant inter-document relationships is important for
several reasons. First, having fewer dimensions enables a
classifier to function much more efficiently, improving both
training and testing time, and also eliminates many noisy
dimensions that could diminish accuracy. Second, informative low-dimension representations can be stored and transmitted more efficiently. Third, low-dimension representations enable high-order processing to be more efficient. For
instance, discovering previously unknown connections between documents can be accomplished more quickly on reduced data [14]. Furthermore, effective pre-processing with
DR may even improve the quality of such analysis tasks by
eliminating noise and by identifying distinct terms with related meaning, as with latent semantic analysis [6]. We intend to further explore such possibilities in future work.
Acknowledgments. Thanks to the USNA Trident Scholar
and ONR In-house Laboratory Independent Research Programs for supporting this work, and to Eric Hardisty and the
anonymous reviewers for their helpful comments.
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